Q. A body moving along a circular path of radius$\ R$ with velocity $v,$ has centripetal acceleration$a$. If its velocity is made equal to 2$v$, then its centripetal acceleration is
A) $4a$
B) $2a$
C) $\frac{a}{4}$
D) $\frac{a}{2}$
Explanation
(a) Centripetal force
$\frac{{mv}^{2}}{R} = ma$
$or\ \ \ \ \ a = \frac{v^{2}}{R}$
$\therefore\ \ \ \ \frac{a_{1}}{a_{2}} = \frac{v_{1}^{2}}{v_{2}^{2}}$
$Here,\ \ v_{1} = v,\ {\ \ v}_{2} = 2v,\ \ a_{1} = a$
$\therefore\ \ \frac{a}{a_{2}} = \frac{v^{2}}{(2v)^{2}} = \frac{1}{4}$
$or\ \ \ a_{2} = 4a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.